Recently, a new parameter of a code, referred to as the remoteness, has been introduced.This parameter can be viewed as a dual to the covering radius. It is exactly determined for the cyclic and dihedral groups. In this paper, we consider the group $U_{6n}$ as a subgroup of $S_{2n+3}$ and obtain its remoteness.  We show that the remoteness of the permutation code $U_{6n}$ is $2n+2$.  Moreover, ...

We fix an integer N ≥ 1 and an elliptic curve E over Z[1/6N ], given by an equation y = f(x) with f(x) a cubic in Z[1/6N ] whose discriminant is invertible in Z[1/6N ]. On E we have the differential of the first kind ω = dx/y and the differential of the second kind η = xdx/y. For each prime p not dividing 6N , we look at this data mod p, and apply the Cartier operator Cp. We get quantities αp, ...

The essential nature of n 3 polyunsaturated fatty acids in neurological development Neural membrane aminophospholipids are characterized by high concentrations of n-3 polyunsaturated fatty acids (PUFA), particularly docosahexaenoic acid (C22:6n-3). For example, adult human cerebral cortex phosphatidylethanolamine (PE) contains 30.5% C22:6n-3 while C22:6n-3 in the retina accounts for 22.2% of PE...

BACKGROUND Despite evidence suggesting roles for caspase-8 (CASP8) -652 6N del and D302H polymorphisms in prostate cancer (PCa), the association of these polymorphisms with PCa risk remains inconclusive. Therefore, a meta-analysis was performed to more precisely estimate the association of CASP8 -652 6N del and D302H polymorphisms with PCa susceptibility. MATERIALS AND METHODS A comprehensive...

This paper gives a new integrable hierarchy of nonlinear evolution equations. In this hierarchy there are the following representative equations: ut = ∂ 5 xu − 2 3 , ut = ∂ 5 x (u 1 3 )xx − 2(u 1 6 )x u ; uxxt + 3uxxux + uxxxu = 0. The first two are in the positive order hierarchy while the 3rd one is in the negative order hierarchy. The whole hierarchy is shown integrable through solving a key...

This paper presents the theoretical elements that support calculation of prime number counting function, π(x), based on properties sequences (6n-1) and (6n+1), n ≥ 1. As a result, Sufficient primality criteria are exposed for terms both deterministic computational algorithm reduces operations in calculating function π(x) by exonerating all multiples 3 from analysis. In analyzing particular term...

The phospholipids, particularly phosphatidylethanolamine, of brain gray matter are enriched with docosahexaenoic acid (22:6n-3). The importance of uptake of preformed 22:6n-3 from plasma compared with synthesis from the alpha-linolenic acid (18:3n-3) precursor in brain is not known. Deficiency of 18:3n-3 results in a compensatory increase in the n-6 docosapentaenoic acid (22:5n-6) in brain, whi...

To investigate the impact of photoreceptor oxidative stress on photoreceptor degeneration in mice carrying the rd8 mutation (C57BL/6N). We compared the hyperoxia-induced proliferative retinopathy (HIPR) model in two mouse strains (C57BL/6J and C57BL/6N). Pups were exposed to 75% oxygen, starting at birth and continuing for 14 days (P14). Mice were euthanized at P14, or allowed to recover in roo...

Several different processes involved in the metabolic fate of docosahexaenoic acid (DHA, C22:6n-3) and its precursor in the biosynthesis route, C24:6n-3, were studied. In cultured skin fibroblasts, the oxidation rate of [1-14C] 24:6n-3 was 2.7 times higher than for [1-14C]22:6n-3, whereas [1-14C]22:6n-3 was incorporated 7 times faster into different lipid classes than was [1-14C]24:6n-3. When d...

Histiocytes are white blood cells of the monocytic lineage and include macrophages and dendritic cells. In patients with a variety of infectious and noninfectious inflammatory disorders, histiocytes can engulf nonapoptotic leukocytes and nonsenescent erythrocytes and thus become hemophagocytes. We report here the identification and characterization of splenic hemophagocytes in a natural model o...